Should the exploration rate be reset after each trial in Q-learning?
The exploration rate, typically parameterized as epsilon / ε, can be changed on every trial. It depends on the complexity of the model and the goals.

The simplest thing to do is keep exploration rate high and fixed. That means the model will continue to explore new options, even at the cost of not "exploiting" the best available option. 

Another option is setting the exploration rate high at the beginning of learning so the model will search the space for possible successful solutions. Then as the model creates a set of policies that are successful for given states, the exploration rate can be lowered or decay. Exploration rate decay can be fixed (i.e., over time there is consistently less exploration and more exploitation). Exploration rate decay can be dynamic and learned. This last option is often the best but also the most complex to implement.

"Dare to Discover: The Effect of the Exploration Strategy on an Agent’s Performance" goes into greater detail on this topic.